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Bilayer materials,assembled by two layers of 2D crystal with weak Van der Waals interactions,revealing unusual properties.We present a continuum model for dislocations in bilayer structure,incorporating elastic energy for each layer and the disregistry between layers,it account for both the inplane and out-of-plane deformations.We show that the buckling of the bilayer structure is crucial to relax the in-plane strains.The obtained structures agree well with the atomistic simulations.